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      First published 2022 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

      Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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      John Wiley & Sons, Inc.

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      © ISTE Ltd 2022

      The rights of Robin Bouclier and Thibault Hirschler to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

      Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.

      Library of Congress Control Number: 2022931519

      British Library Cataloguing-in-Publication Data

      A CIP record for this book is available from the British Library

      ISBN 978-1-78630-824-5

      Preface

      P.1. The book series

      This book constitutes the first volume of the set of books entitled “IsoGeometric Analysis (IGA) tools for optimization applications in structural mechanics”. The objective of the series is to present, in a comprehensive and detailed manner, some advanced modeling and numerical strategies, recently developed in the context of IGA, that provide strong benefits not only for direct simulations but also for the resolution of optimization problems in structural mechanics. The IGA paradigm was originally introduced by Hughes and co-workers in 2005 (Hughes et al. 2005) to reunify the fields of computer-aided design (CAD) and finite element analysis (FEA). The core idea is to resort to the same higher-order and smooth spline bases for the representation of the geometry in CAD as well as for the approximation of solutions fields in FEA. The use of such families of functions quickly made IGA highly attractive for two main reasons: first, a common geometrical model can be used by both the designers and analysts; second, an increased per-degree-of-freedom (per-DOF) accuracy can be reached in comparison to standard finite element methods (FEM). This technology is thus often seen as a high-performance computational tool.

      This first volume tackles design optimization that is essential to reduce the usual long trial-and-error learning process during the product development in industry. More precisely, we focus on structural shape optimization, which aims at finding the optimal shape of a given topology of a structure with respect to a certain objective, such as minimal mass and maximal rigidity. Shape optimization undoubtedly constitutes one of the most valuable applications for IGA as the latter combines high-quality geometric representations and efficient analysis capabilities into one single model. In this book, we seek to develop a full analysis-to-optimization framework that is applicable to complex structures in order to tend to real-world (industrial) applications.

      From an analysis point of view, this forces us to face two very important challenges encountered in the field today, namely (i) the simple local enrichment of rigid tensor-product spline models (which may also go with trimming when introducing an arbitrary local region within a spline patch) and (ii) the efficient analysis of large multipatch structures. The methods proposed to answer these issues are quite original for the domain and are based on developments in which the French community is particularly active. More precisely, the strategies rely on domain coupling and, in particular: (i) global/local non-invasive coupling algorithms that enable us to locally enrich a global model without altering its corresponding numerical operators and (ii) parallel domain decomposition solvers that allow us to separate the computational resources between several subdomains.

      P.2.1. Intended audience

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